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for the sphere problem, the magnetic field values need to be calculated wrt the center of the sphere. analytics abbreviate to Ana

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This commit is contained in:
Lindsey
2015-08-06 16:40:19 -07:00
parent 668e435cce
commit 203640c803
2 changed files with 15 additions and 13 deletions
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simpegPF/MagAnalytics.py
+13 -11
View File
@@ -15,11 +15,11 @@ def spheremodel(mesh, x0, y0, z0, r):
def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag='total'):
"""
test
Analytic function for Magnetics problem. The set up here is
magnetic sphere in whole-space.
magnetic sphere in whole-space assuming that the inducing field is oriented in the x-direction.
* (x0,y0,z0)
* (x0, y0, z0 ): is the center location of sphere
@@ -31,6 +31,8 @@ def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
"""
print H0
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
@@ -47,7 +49,7 @@ def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
# Inside of the sphere
rf2 = 3*mu1/(mu2+2*mu1)
if (flag == 'total'):
if flag is 'total' and any(ind):
Bx[ind] = mu2*H0*(rf2)
elif (flag == 'secondary'):
Bx[ind] = mu2*H0*(rf2)-mu1*H0
@@ -57,12 +59,12 @@ def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
# Outside of the sphere
rf1 = (mu2-mu1)/(mu2+2*mu1)
if (flag == 'total'):
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
elif (flag == 'secondary'):
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*y[~ind]))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*z[~ind]))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(y[~ind]-y0)))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(z[~ind]-z0)))
return np.reshape(Bx, x.shape, order='F'), np.reshape(By, x.shape, order='F'), np.reshape(Bz, x.shape, order='F')
@@ -124,7 +126,7 @@ def CongruousMagBC(mesh, Bo, chi):
return np.r_[Bbcx, Bbcy, Bbcz], (1/gamma-1/(3+gamma))*1/V
def MagSphereAnalFunA(x, y, z, R, xc, yc, zc, chi, Bo, flag):
def MagSphereAnaFunA(x, y, z, R, xc, yc, zc, chi, Bo, flag):
"""
Computing boundary condition using Congrous sphere method.
This is designed for secondary field formulation.
@@ -210,9 +212,9 @@ if __name__ == '__main__':
flag = 'secondary'
Box = 1.
H0 = Box/mu_0
Bbcxx, Bbcxy, Bbcxz = MagSphereAnalFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcyx, Bbcyy, Bbcyz = MagSphereAnalFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbczx, Bbczy, Bbczz = MagSphereAnalFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcxx, Bbcxy, Bbcxz = MagSphereAnaFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcyx, Bbcyy, Bbcyz = MagSphereAnaFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbczx, Bbczy, Bbczz = MagSphereAnaFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbc_anal = np.r_[Bbcxx, Bbcyy, Bbczz]
# fig, ax = plt.subplots(1,1, figsize = (10, 10))
simpegPF/Tests/test_forward_PFproblem.py
+2 -2
View File
@@ -26,7 +26,7 @@ class MagFwdProblemTests(unittest.TestCase):
self.chi = chi
def test_anal_forward(self):
def test_ana_forward(self):
survey = PF.BaseMag.BaseMagSurvey()
@@ -47,7 +47,7 @@ class MagFwdProblemTests(unittest.TestCase):
u = self.prob.fields(self.chi)
B = u['B']
bxa,bya,bza = PF.MagAnalytics.MagSphereAnalFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],100.,0.,0.,0.,0.01, b0,'secondary')
bxa,bya,bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],100.,0.,0.,0.,0.01, b0,'secondary')
dpred = survey.projectFieldsAsVector(B)
err = np.linalg.norm(dpred-np.r_[bxa, bya, bza])/np.linalg.norm(np.r_[bxa, bya, bza])